Challenge mode is one of the new modes introduced in Xbox 360/PS3 port which have 30 different challenges to beat (ten for each course). As for the challenges themselves, they are relatively simple, ranging from "reach checkpoint in time" to "hit 10 traffic cones". You can also view demonstration from each challenge, which is neat.
Personally the biggest problem I have with this mode is that challenges are tied to certain transmission. And unfortunately for me 75% of challenges are using Automatic transmission, which I find rather hard to get used to, as you can't do gear drifting with them. It would have been better to give player a choice which transmission they want to use.
Also the challenges are relatively easy to beat (although frankly few of them took few attempts to get right). The rival challenges especially are cakewalk compared to Arcade mode races, which I found bit weird.
This was recorded on Elgato HD60 via using component-to-HDMI adapter.